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Publisher: Cambridge University Press   (Total: 371 journals)

 Compositio MathematicaJournal Prestige (SJR): 3.139 Citation Impact (citeScore): 1Number of Followers: 1      Subscription journal ISSN (Print) 0010-437X - ISSN (Online) 1570-5846 Published by Cambridge University Press  [371 journals]
• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$K$ ++++++++++++ ++++++++ ++++-theory+revisited&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2018&rft.volume=154&rft.spage=1801&rft.epage=1814&rft.aulast=Tamme&rft.aufirst=Georg&rft.au=Georg+Tamme&rft_id=info:doi/10.1112/S0010437X18007236">Excision in algebraic $K$ -theory revisited
• Authors: Georg Tamme
Pages: 1801 - 1814
Abstract: By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic $K$ -theory. We give a new and direct proof of Suslin’s result based on an exact sequence of categories of perfect modules. In fact, we prove a more general descent result for a pullback square of ring spectra and any localizing invariant. Our descent theorem contains not only Suslin’s result, but also Nisnevich descent of algebraic $K$ -theory for affine schemes as special cases. Moreover, the role of the Tor-unitality condition becomes very transparent.
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007236
Issue No: Vol. 154, No. 9 (2018)

• On multi-pointed non-commutative deformations and Calabi–Yau
threefolds
• Authors: Yujiro Kawamata
Pages: 1815 - 1842
Abstract: We will develop a theory of multi-pointed non-commutative deformations of a simple collection in an abelian category, and construct relative exceptional objects and relative spherical objects in some cases. This is inspired by a work by Donovan and Wemyss.
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007248
Issue No: Vol. 154, No. 9 (2018)

• Applications of the hyperbolic Ax–Schanuel conjecture
• Authors: Christopher Daw; Jinbo Ren
Pages: 1843 - 1888
Abstract: In 2014, Pila and Tsimerman gave a proof of the Ax–Schanuel conjecture for the $j$ -function and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura variety. We refer to this generalization as the hyperbolic Ax–Schanuel conjecture. In this article, we show that the hyperbolic Ax–Schanuel conjecture can be used to reduce the Zilber–Pink conjecture for Shimura varieties to a problem of point counting. We further show that this point counting problem can be tackled in a number of cases using the Pila–Wilkie counting theorem and several arithmetic conjectures. Our methods are inspired by previous applications of the Pila–Zannier method and, in particular, the recent proof by Habegger and Pila of the Zilber–Pink conjecture for curves in abelian varieties.
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X1800725X
Issue No: Vol. 154, No. 9 (2018)

• The Manin constant in the semistable case
• Authors: Kęstutis Česnavičius
Pages: 1889 - 1920
Abstract: For an optimal modular parametrization $J_{0}(n){\twoheadrightarrow}E$ of an elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$ , Manin conjectured the agreement of two natural $\mathbb{Z}$ -lattices in the $\mathbb{Q}$ -vector space $H^{0}(E,\unicode[STIX]{x1D6FA}^{1})$ . Multiple authors generalized his conjecture to higher-dimensional newform quotients. We prove the Manin conjecture for semistable $E$ , give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral $p$ -adic étale and de Rham cohomologies of abelian varieties over $p$ -adic fields and exhibit a new exactness result for Néron models.
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007273
Issue No: Vol. 154, No. 9 (2018)

• Four-fold Massey products in Galois cohomology
• Authors: Pierre Guillot; Ján Mináč, Adam Topaz
Pages: 1921 - 1959
Abstract: In this paper, we develop a new necessary and sufficient condition for the vanishing of $4$ -Massey products of elements in the modulo- $2$ Galois cohomology of a field. This new description allows us to define a splitting variety for $4$ -Massey products, which is shown in the appendix to satisfy a local-to-global principle over number fields. As a consequence, we prove that, for a number field, all such $4$ -Massey products vanish whenever they are defined. This provides new explicit restrictions on the structure of absolute Galois groups of number fields.
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007297
Issue No: Vol. 154, No. 9 (2018)

• Composite quasianalytic functions
• Authors: André Belotto da Silva; Edward Bierstone, Michael Chow
Pages: 1960 - 1973
Abstract: We prove two main results on Denjoy–Carleman classes: (1) a composite function theorem which asserts that a function $f(x)$ in a quasianalytic Denjoy–Carleman class ${\mathcal{Q}}_{M}$ , which is formally composite with a generically submersive mapping $y=\unicode[STIX]{x1D711}(x)$ of class ${\mathcal{Q}}_{M}$ , at a single given point in the source (or in the target) of $\unicode[STIX]{x1D711}$ can be written locally as $f=g\circ \unicode[STIX]{x1D711}$ , where $g(y)$ belongs to a shifted Denjoy–Carleman class ${\mathcal{Q}}_{M^{(p)}}$ ; (2) a statement on a similar loss of regularity for functions definable in the $o$ -minimal structure given by expansion of the real field by restricted functions of quasianalytic class ${\mathcal{Q}}_{M}$ . Both results depend on an estimate for the regularity of a
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007339
Issue No: Vol. 154, No. 9 (2018)

• Dieudonné theory over semiperfect rings and perfectoid rings
• Authors: Eike Lau
Pages: 1974 - 2004
Abstract: The Dieudonné crystal of a $p$ -divisible group over a semiperfect ring $R$ can be endowed with a window structure. If $R$ satisfies a boundedness condition, this construction gives an equivalence of categories. As an application we obtain a classification of $p$ -divisible groups and commutative finite locally free $p$ -group schemes over perfectoid rings by Breuil–Kisin–Fargues modules if $p\geqslant 3$ .
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007352
Issue No: Vol. 154, No. 9 (2018)

• Stability of products of equivalence relations
• Authors: Amine Marrakchi
Pages: 2005 - 2019
Abstract: An ergodic probability measure preserving (p.m.p.) equivalence relation ${\mathcal{R}}$ is said to be stable if ${\mathcal{R}}\cong {\mathcal{R}}\times {\mathcal{R}}_{0}$ where ${\mathcal{R}}_{0}$ is the unique hyperfinite ergodic type $\text{II}_{1}$ equivalence relation. We prove that a direct product ${\mathcal{R}}\times {\mathcal{S}}$ of two ergodic p.m.p. equivalence relations is stable if and only if one of the two components ${\mathcal{R}}$ or ${\mathcal{S}}$ is stable. This result is deduced from a new local characterization of stable equivalence relations. The similar question on McDuff $\text{II}_{1}$ factors is also discussed and some partial results are given.
PubDate: 2018-09-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007388
Issue No: Vol. 154, No. 9 (2018)

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